Consider two ideal gases X and Y at a given temperature. Gas X is a rigid diatomic gas. Gas Y is a non-linear polyatomic gas having two active vibrational modes. If _X and _Y represent the ratio of specific heats ( C_p/C_v ) for gas X and gas Y respectively, the ratio _X _Y is:

Step-by-step solution

For gas X (rigid diatomic gas): Degrees of freedom, f_X = 3 (translational) + 2 (rotational) = 5 _X = 1 + 2 f_X = 1 + 2 5 = 7 5 For gas Y (non-linear polyatomic gas with two active vibrational modes): Each vibrational mode contributes 2 degrees of freedom (one for kinetic energy and one for potential energy). Degrees of freedom, f_Y = 3 (translational) + 3 (rotational) + 2 2 (vibrational) = 10 _Y = 1 + 2 f_Y = 1 + 2 10 = 6 5 Ratio _X _Y = 7/5 6/5 = 7 6 Answer: 7 6